Hello dear researchers,
are there any other methods that calculates the real component from the imaginary component and vice versa of a complex function different than the Kramers-Kronig relations and Hilbert transforms ?
I would like to couple the real and the imaginary parts of a dispersive function with stochastic values.
Z= Re(Z)+i*Im(Z) where Z is a complex number and i=√(-1), Re(Z) is the real part of Z and Im(Z) is the imaginary part of Z. The magnitude of Z is given by /Z/= √[(Re(Z)) *(Re(Z))+(Im(Z))*(Im(Z))]. The relationship between the real and imaginary parts of Z is therefore in terms of /Z/ as Im(Z) = √[/Z/*/Z/-Re(Z)*Re(Z)].
Ette Etuk
thanks for your answer, I already know these relations that you wrote, but this is not what i meant by my question. For sintance the Kramers-Kronig relations find a mathematical relation the demonstrate the dependency of the two components (real and imaginary) on each other for any dispersion relation , e.g dispersion in optics, or materials.
Not clear what you have in mind. Something like the fluctuation-dissipation theorem?
S. Alexious, in the dispersion phenomenon in the medium, the properties of the medium such as permittivity, permeability, impedance, etc. are dispersive as well, which means that they are functions of frequency and hence they have a real and an imaginary component. These components rely on each other, therefore the hilbert transforms or the Kramers Kronig relations prove this relation between the real and the imaginary components through mathenatical equations.
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